Timberland Project Report
Yijia Yu
18/06/2020
1. Introduction
Timberland investment instruments are often used as an alternative asset class in the public and private pension fund managers’ portfolios. As a long-term investment, timberland assets have the benefits of low correlation to the stock market, portfolio diversification, and inflation hedging. Therefore, timberland assets not only make the portfolio more diversified but also reduce the volatility. A powerful component of timberland return drivers is biological growth, which is independent of all factors typically impacting other investments and makes timberland assets distinguishing from others.
Since the COVID-19 was declared a pandemic on March 11th, 2020, the world experienced the most severe economic recession since the great depression. In the first two quarters of 2020, the annual rate of growth in Canadian real GDP has dropped nearly 20%. Beginning on February 2020, stock markets worldwide became extremely volatile, with all major Wall Street in- dices experiencing their worst drop since 1987 followed by a quick rebound. Timberland as a alternative real asset becomes increasing popular for some Canadian pension-fund managers, as this kind of illiquid asset can provide institutional investors with strong diversification benefits and stable valuations.
Timberland Industry in Canada
The forestry industry is an important contributor to Canada’s economy, generating $25.8 billion to Canada’s GDP in 2018 and directly employing about 1209,940 people across the country. The forestry industry contributed 8% export in 2018 and generated $2.9 billion revenues for provincial, territorial and federal governments in 2017. Top export markets for Canadian forestry are the United States (66%) and China (15%) in 2018. Stronger Canadian lumber and plup demand stimulated by U.S. housing starts and other industry demand makes a promising perspective for the Canadian forestry markets.
The majority of Canada’s forests are owned by the provinces in which they are located, with just 1.6 percent being owned federally. The provincial and territorial governments are responsible for managing forest conservation, with strict laws in place to shape forest practices. These stringent laws are particularly important when it comes to halting logging practices and encouraging reforestation, as extensive deforestation was carried out by European settlers in Canada throughout the 18th and 19th centuries.
The wood product manufacturing sector is the most lucrative of the forestry industries, with a nominal GDP of approximately 11 billion Canadian dollars in 2017. Western Forest Products, a lumber company based in British Columbia, is one of the key players in the forestry industry with an annual revenue of around 1.2 billion Canadian dollars in 2018. As a result, British Columbia employs by far the most people in the forestry and logging industry, followed by Quebec.
The United States is the main trading partner of Canada when it comes to forest resources, with Canadian exports worth around 24.24 billion Canadian dollars in 2017. Lumber, sawmill and millwork products are the most traded Canadian forest products, with exports worth just over 15 billion Canadian dollars in 2018 globally.
In spite of today’s challenging economic environment, the long-term supply and demand fundamentals of timberland bode well for the patient investor who thinks in terms of decades and not quarters. A growing Canadian and global population with a rising standard of living will continue to increase demand on a finite supply of timberland.
About this study
The main purpose of this study is to investigate long-term financial performance for timberland asset in a mixed-asset portfolio. The modern portfolio theory will be used to construct the optimal portfolios, and to analyze its diversification effects. In order to find the time-varying optimized allocations, time-series GARCH model will be used.
Data used in this study
- Private timberland market
Returns of private equity timberland investment performance is approximated by the NCREIF Timberland Index (NTI), which is a quarterly time series composite return measure of investment performance of a large pool of individual U.S. timber properties acquired in the private market for investment purposes only.
- Public timberland market
As of July 2019, there is four publicly traded REITs that specialize in timberland. Together, they own more than 17 million acres of timberland properties in the U.S., Canada, New Zealand and other locations. The four REITs compose the timber sector of the FTSE NAREIT All REIT index are listed below:
- Potlatch
- CatchMark
- Rayonier
- Weyerhaeuser
- To examine the role of timberland assets in a mixed portfolio, assets including large-cap stocks, small-cap stocks, returns of private- and public-equaty real estate, treasury bonds, and treasury bills are considered in this study. Returns on those asset classes are approximated by the S&P 500 Index (SP500), Russell 2000 Index (RU2000), National Council of Real Estate Investment Fiduciaries Property Index (NPI) and National Association of Real Estate Investment Trust (NAREIT) 10-Year Treasury bonds yield, and 3-month treasury bills respectively.
3. Results
3.1 Descriptive analysis
This is a interactively graphical representation of selected quarterly return indices from 1987 Q1 to 2020 Q1. Some clear pattern could be observed. First, NCREIF is much less volatile than REIT, SP500, RU2000. Second, REIT follows SP500 closely but NTI doesn’t. For example, both REIT and SP500 suffered from a big loss during 2008 financial crisis, whereas NCREIF kept a positive returns until 2009/Q2, where they only got a slightly negative return value. Some people said it’s because timberland market tends to lag the public equity market. But some also argues that it’s because of the biological growth of trees wouldn’t stop as the market went into depression.
The unconditional correlations of the return series were studied by calculating the correlation coefficients and by plotting the pairwise scatter plots, as showed in the following graph. In this portfolio, the correlation of NCREIF with all financial assets are uniformly low, except for the 3 month Treasury bill (CA). The correlation between big cap (SP500) and small cap (RU2000) are highly significant, and they’re almost linearly correlated. Unlike private timber market, the timber REITs shows a closely correlation with the stock market and 10 year treasury bonds. Returns on most asset classes are positively skewed. However, by using the Jarque-Bera test statistic, most of asset returns are not normally distributed.
Summary statistics of all asset classes from 1987 Q1 to 2010 Q1 are reported in the following table. On a quarterly basis, NTI (private timberland index) has the highest mean return of 2.71% and a moderate standard deviation of 3.78%. Timber REITs have a highest standard deviation but a relative lower mean of 2.06%. Treasury bills have both lowest return and standard deviation.
## n mean sd median trimmed mad min max range skew
## NTI 133 2.71 3.78 1.53 2.07 1.51 -6.54 22.34 28.88 2.13
## NPI 133 1.90 2.09 2.11 2.18 1.13 -8.29 5.43 13.72 -2.23
## SP500 133 2.06 7.00 2.69 2.46 5.38 -23.77 21.75 45.52 -0.66
## RU2000 133 2.11 9.49 2.99 2.73 7.87 -29.90 29.05 58.95 -0.61
## T-bonds10Y 133 1.54 2.30 1.48 1.51 2.50 -3.39 8.04 11.42 0.14
## NAREIT 133 1.07 8.63 0.99 1.30 6.95 -31.08 21.37 52.44 -0.61
## Timber REITs 133 1.41 10.64 2.15 1.66 8.02 -29.44 37.00 66.44 -0.18
## T-bills3M 133 4.00 3.35 3.22 3.54 3.31 0.16 13.51 13.35 1.03
## kurtosis se
## NTI 6.73 0.33
## NPI 7.24 0.18
## SP500 1.21 0.61
## RU2000 1.02 0.82
## T-bonds10Y -0.43 0.20
## NAREIT 1.93 0.75
## Timber REITs 1.21 0.92
## T-bills3M 0.33 0.29Three risk measures are applied to individual asset, and the results are reported in the following table.
## NTI NPI SP500 RU2000 T-bonds10Y NAREIT
## SD 0.037831038 0.02091420 0.06997736 0.0948503 0.02296899 0.08630959
## VaR -0.003228681 -0.02349186 -0.10482225 -0.1481524 -0.02142671 -0.14178418
## CVaR -0.107178392 -0.05549443 -0.15902461 -0.2174900 -0.02867964 -0.22446137
## Timber REITs T-bills3M
## SD 0.1064128 0.033524621
## VaR -0.1631146 -0.004021242
## CVaR -0.2369724 -0.018686743## $NTI
##
## Augmented Dickey-Fuller Test
##
## data: newX[, i]
## Dickey-Fuller = -3.9265, Lag order = 5, p-value = 0.01501
## alternative hypothesis: stationary
##
##
## $NPI
##
## Augmented Dickey-Fuller Test
##
## data: newX[, i]
## Dickey-Fuller = -4.2311, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
##
##
## $SP500
##
## Augmented Dickey-Fuller Test
##
## data: newX[, i]
## Dickey-Fuller = -3.2387, Lag order = 5, p-value = 0.08451
## alternative hypothesis: stationary
##
##
## $RU2000
##
## Augmented Dickey-Fuller Test
##
## data: newX[, i]
## Dickey-Fuller = -4.661, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
##
##
## $`T-bonds10Y`
##
## Augmented Dickey-Fuller Test
##
## data: newX[, i]
## Dickey-Fuller = -5.3722, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
##
##
## $NAREIT
##
## Augmented Dickey-Fuller Test
##
## data: newX[, i]
## Dickey-Fuller = -4.2638, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
##
##
## $`Timber REITs`
##
## Augmented Dickey-Fuller Test
##
## data: newX[, i]
## Dickey-Fuller = -5.5139, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
##
##
## $`T-bills3M`
##
## Augmented Dickey-Fuller Test
##
## data: newX[, i]
## Dickey-Fuller = -2.9806, Lag order = 5, p-value = 0.1687
## alternative hypothesis: stationary## $NTI
##
## Phillips-Perron Unit Root Test
##
## data: newX[, i]
## Dickey-Fuller Z(alpha) = -177.73, Truncation lag parameter = 4, p-value
## = 0.01
## alternative hypothesis: stationary
##
##
## $NPI
##
## Phillips-Perron Unit Root Test
##
## data: newX[, i]
## Dickey-Fuller Z(alpha) = -29.936, Truncation lag parameter = 4, p-value
## = 0.01
## alternative hypothesis: stationary
##
##
## $SP500
##
## Phillips-Perron Unit Root Test
##
## data: newX[, i]
## Dickey-Fuller Z(alpha) = -137.98, Truncation lag parameter = 4, p-value
## = 0.01
## alternative hypothesis: stationary
##
##
## $RU2000
##
## Phillips-Perron Unit Root Test
##
## data: newX[, i]
## Dickey-Fuller Z(alpha) = -139.91, Truncation lag parameter = 4, p-value
## = 0.01
## alternative hypothesis: stationary
##
##
## $`T-bonds10Y`
##
## Phillips-Perron Unit Root Test
##
## data: newX[, i]
## Dickey-Fuller Z(alpha) = -122.7, Truncation lag parameter = 4, p-value
## = 0.01
## alternative hypothesis: stationary
##
##
## $NAREIT
##
## Phillips-Perron Unit Root Test
##
## data: newX[, i]
## Dickey-Fuller Z(alpha) = -117.06, Truncation lag parameter = 4, p-value
## = 0.01
## alternative hypothesis: stationary
##
##
## $`Timber REITs`
##
## Phillips-Perron Unit Root Test
##
## data: newX[, i]
## Dickey-Fuller Z(alpha) = -139.21, Truncation lag parameter = 4, p-value
## = 0.01
## alternative hypothesis: stationary
##
##
## $`T-bills3M`
##
## Phillips-Perron Unit Root Test
##
## data: newX[, i]
## Dickey-Fuller Z(alpha) = -13.822, Truncation lag parameter = 4, p-value
## = 0.3184
## alternative hypothesis: stationary
3.2 Portfolio Optimization
## # A tibble: 6 x 9
## index NTI NPI SP500 RU2000 `T-bonds10Y` NAREIT `Timber REITs`
## <yea> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1987… -6.00e-4 0.0183 0.138 0.170 0.0148 0.0177 0.370
## 2 1987… 4.91e-2 0.0119 0.0631 0.00857 -0.0189 0.0122 -0.134
## 3 1987… 1.19e-1 0.0209 0.0412 0.0212 -0.0292 -0.0646 0.0301
## 4 1987… 7.85e-2 0.0267 -0.238 -0.299 0.0584 -0.124 -0.224
## 5 1988… 3.98e-2 0.0184 -0.00539 0.124 0.0358 0.0218 -0.00876
## 6 1988… 6.33e-2 0.02 0.0383 0.0432 0.00986 -0.00939 0.0141
## # … with 1 more variable: `T-bills3M` <dbl>## Warning in whichFormat(charvec[1]): character string is not in a standard
## unambiguous format##
## Title:
## Portfolio Constraints
##
## Lower/Upper Bounds:
## NTI NPI SP500 RU2000 T-bonds10Y NAREIT Timber REITs T-bills3M
## Lower 0 0 0 0 0 0 0 0
## Upper 1 1 1 1 1 1 1 1
##
## Equal Matrix Constraints:
## ceq NTI NPI SP500 RU2000 T-bonds10Y NAREIT Timber REITs T-bills3M
## Budget -1 -1 -1 -1 -1 -1 -1 -1 -1
## attr(,"na.action")
## Return
## 1
## attr(,"class")
## [1] "omit"
##
## Cardinality Constraints:
## NTI NPI SP500 RU2000 T-bonds10Y NAREIT Timber REITs T-bills3M
## Lower 0 0 0 0 0 0 0 0
## Upper 1 1 1 1 1 1 1 1##
## Title:
## MV Feasible Portfolio
## Estimator: covEstimator
## Solver: solveRquadprog
## Optimize: minRisk
## Constraints: LongOnly
##
## Portfolio Weights:
## NTI NPI SP500 RU2000 T-bonds10Y NAREIT
## 0.125 0.125 0.125 0.125 0.125 0.125
## Timber REITs T-bills3M
## 0.125 0.125
##
## Covariance Risk Budgets:
## NTI NPI SP500 RU2000 T-bonds10Y NAREIT
## 0.0201 0.0095 0.1912 0.2785 -0.0022 0.2084
## Timber REITs T-bills3M
## 0.2807 0.0137
##
## Target Returns and Risks:
## mean Cov CVaR VaR
## 0.0210 0.0386 0.0817 0.0574
##
## Description:
## Mon Aug 24 16:21:11 2020 by user:
##
## Title:
## MV Efficient Portfolio
## Estimator: covEstimator
## Solver: solveRquadprog
## Optimize: minRisk
## Constraints: LongOnly
##
## Portfolio Weights:
## NTI NPI SP500 RU2000 T-bonds10Y NAREIT
## 0.0517 0.4510 0.0000 0.0323 0.3345 0.0000
## Timber REITs T-bills3M
## 0.0012 0.1293
##
## Covariance Risk Budgets:
## NTI NPI SP500 RU2000 T-bonds10Y NAREIT
## 0.0543 0.4435 0.0000 0.0323 0.3188 0.0000
## Timber REITs T-bills3M
## 0.0012 0.1499
##
## Target Returns and Risks:
## mean Cov CVaR VaR
## 0.0210 0.0130 0.0124 -0.0014
##
## Description:
## Mon Aug 24 16:21:11 2020 by user:
##
## Title:
## MV Tangency Portfolio
## Estimator: covEstimator
## Solver: solveRquadprog
## Optimize: minRisk
## Constraints: LongOnly
##
## Portfolio Weights:
## NTI NPI SP500 RU2000 T-bonds10Y NAREIT
## 0.0359 0.4408 0.0000 0.0296 0.2199 0.0000
## Timber REITs T-bills3M
## 0.0000 0.2738
##
## Covariance Risk Budgets:
## NTI NPI SP500 RU2000 T-bonds10Y NAREIT
## 0.0400 0.3448 0.0000 0.0257 0.1393 0.0000
## Timber REITs T-bills3M
## 0.0000 0.4502
##
## Target Returns and Risks:
## mean Cov CVaR VaR
## 0.0244 0.0141 0.0116 -0.0053
##
## Description:
## Mon Aug 24 16:21:11 2020 by user:
##
## Title:
## MV Portfolio Frontier
## Estimator: covEstimator
## Solver: solveRquadprog
## Optimize: minRisk
## Constraints: LongOnly
## Portfolio Points: 5 of 25
##
## Portfolio Weights:
## NTI NPI SP500 RU2000 T-bonds10Y NAREIT Timber REITs T-bills3M
## 1 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000
## 7 0.0679 0.4576 0.0007 0.0275 0.4346 0.0000 0.0108 0.0009
## 13 0.0311 0.4376 0.0000 0.0284 0.1843 0.0000 0.0000 0.3186
## 19 0.0000 0.3305 0.0000 0.0207 0.0000 0.0000 0.0000 0.6488
## 25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
##
## Covariance Risk Budgets:
## NTI NPI SP500 RU2000 T-bonds10Y NAREIT Timber REITs T-bills3M
## 1 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000
## 7 0.0521 0.4459 0.0006 0.0253 0.4638 0.0000 0.0119 0.0004
## 13 0.0337 0.3070 0.0000 0.0227 0.0979 0.0000 0.0000 0.5387
## 19 0.0000 0.0619 0.0000 0.0065 0.0000 0.0000 0.0000 0.9316
## 25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000
##
## Target Returns and Risks:
## mean Cov CVaR VaR
## 1 0.0107 0.0863 0.2102 0.1236
## 7 0.0180 0.0133 0.0146 0.0041
## 13 0.0254 0.0148 0.0115 -0.0064
## 19 0.0327 0.0221 0.0083 -0.0079
## 25 0.0400 0.0335 -0.0028 -0.0043
##
## Description:
## Mon Aug 24 16:21:11 2020 by user:
GARCH model estimation, Backtesting the risk model and Forecasting
## Series: xts.nti
## ARIMA(1,1,2)
##
## Coefficients:
## ar1 ma1 ma2
## -0.9517 0.0345 -0.6404
## s.e. 0.0473 0.1038 0.1170
##
## sigma^2 estimated as 0.001036: log likelihood=267.04
## AIC=-526.08 AICc=-525.77 BIC=-514.55
##
## Ljung-Box test
##
## data: Residuals from ARIMA(1,1,2)
## Q* = 7.0216, df = 5, p-value = 0.219
##
## Model df: 3. Total lags used: 8## Series: xts.npi
## ARIMA(2,0,2)(0,0,2)[4] with non-zero mean
##
## Coefficients:
## ar1 ar2 ma1 ma2 sma1 sma2 mean
## 1.4429 -0.7121 -0.6924 0.4407 0.5504 0.1771 0.0187
## s.e. 0.1290 0.1038 0.1408 0.0985 0.1120 0.0922 0.0044
##
## sigma^2 estimated as 0.0001201: log likelihood=413.99
## AIC=-811.97 AICc=-810.81 BIC=-788.85
##
## Ljung-Box test
##
## data: Residuals from ARIMA(2,0,2)(0,0,2)[4] with non-zero mean
## Q* = 0.38528, df = 3, p-value = 0.9433
##
## Model df: 7. Total lags used: 10##
## ARIMA(2,0,2)(1,0,1)[4] with non-zero mean : Inf
## ARIMA(0,0,0) with non-zero mean : -209.7397
## ARIMA(1,0,0)(1,0,0)[4] with non-zero mean : -204.2254
## ARIMA(0,0,1)(0,0,1)[4] with non-zero mean : -205.1085
## ARIMA(0,0,0) with zero mean : -212.2985
## ARIMA(0,0,0)(1,0,0)[4] with non-zero mean : -206.4223
## ARIMA(0,0,0)(0,0,1)[4] with non-zero mean : -206.218
## ARIMA(0,0,0)(1,0,1)[4] with non-zero mean : -203.2036
## ARIMA(1,0,0) with non-zero mean : -207.7368
## ARIMA(0,0,1) with non-zero mean : -208.6271
## ARIMA(1,0,1) with non-zero mean : Inf
##
## Best model: ARIMA(0,0,0) with zero mean
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,0,0) with zero mean
## Q* = 6.5488, df = 8, p-value = 0.586
##
## Model df: 0. Total lags used: 8##
## Box-Ljung test
##
## data: model.arima$residuals^2
## X-squared = 24.212, df = 12, p-value = 0.01903##
## Box-Ljung test
##
## data: model.arima2$residuals^2
## X-squared = 5.6893, df = 12, p-value = 0.9309##
## Box-Ljung test
##
## data: model.arima3$residuals^2
## X-squared = 1.8949, df = 12, p-value = 0.9996## [1] 0.002018172
## [1] 1.529996e-10
## [1] 0.3906977
## [1] 0.7446981
## [1] 0.8463008
## [1] 0.009205018
## [1] 0.8986624
## [1] 0## Loading required package: parallel##
## Attaching package: 'rugarch'## The following object is masked from 'package:purrr':
##
## reduce## The following object is masked from 'package:stats':
##
## sigma##
## Fitting models using approximations to speed things up...
##
## ARIMA(2,0,2) with non-zero mean : -11942.31
## ARIMA(0,0,0) with non-zero mean : -11971.15
## ARIMA(1,0,0) with non-zero mean : -11963.77
## ARIMA(0,0,1) with non-zero mean : -11964.52
## ARIMA(0,0,0) with zero mean : -10316.91
## ARIMA(1,0,1) with non-zero mean : -11956.67
##
## Now re-fitting the best model(s) without approximations...
##
## ARIMA(0,0,0) with non-zero mean : -11971.15
##
## Best model: ARIMA(0,0,0) with non-zero mean## Series: simseries
## ARIMA(0,0,0) with non-zero mean
##
## Coefficients:
## mean
## 0.0098
## s.e. 0.0002
##
## sigma^2 estimated as 6.067e-05: log likelihood=5993.04
## AIC=-11982.08 AICc=-11982.07 BIC=-11971.15##
## Fitting models using approximations to speed things up...
##
## ARIMA(2,0,2) with non-zero mean : -14451.07
## ARIMA(0,0,0) with non-zero mean : -14480.05
## ARIMA(1,0,0) with non-zero mean : -14472.45
## ARIMA(0,0,1) with non-zero mean : -14472.7
## ARIMA(0,0,0) with zero mean : -12096.21
## ARIMA(1,0,1) with non-zero mean : -14464.86
##
## Now re-fitting the best model(s) without approximations...
##
## ARIMA(0,0,0) with non-zero mean : -14480.05
##
## Best model: ARIMA(0,0,0) with non-zero mean## Series: simseries
## ARIMA(0,0,0) with non-zero mean
##
## Coefficients:
## mean
## 0.0098
## s.e. 0.0001
##
## sigma^2 estimated as 4.17e-05: log likelihood=7247.62
## AIC=-14491.25 AICc=-14491.24 BIC=-14480.05##
## please wait...calculating quantiles...
## VaR Backtest Report
## ===========================================
## Model: eGARCH-std
## Backtest Length: 1000
## Data:
##
## ==========================================
## alpha: 1%
## Expected Exceed: 10
## Actual VaR Exceed: 13
## Actual %: 1.3%
##
## Unconditional Coverage (Kupiec)
## Null-Hypothesis: Correct Exceedances
## LR.uc Statistic: 0.831
## LR.uc Critical: 6.635
## LR.uc p-value: 0.362
## Reject Null: NO
##
## Conditional Coverage (Christoffersen)
## Null-Hypothesis: Correct Exceedances and
## Independence of Failures
## LR.cc Statistic: 2.833
## LR.cc Critical: 9.21
## LR.cc p-value: 0.243
## Reject Null: NO
##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: eGARCH
## Horizon: 12
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=2020 Q1]:
## Series Sigma
## T+1 0.01004 0.010373
## T+2 0.01004 0.010281
## T+3 0.01004 0.010192
## T+4 0.01004 0.010107
## T+5 0.01004 0.010025
## T+6 0.01004 0.009946
## T+7 0.01004 0.009871
## T+8 0.01004 0.009799
## T+9 0.01004 0.009729
## T+10 0.01004 0.009662
## T+11 0.01004 0.009598
## T+12 0.01004 0.009536
##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: eGARCH
## Horizon: 10
## Roll Steps: 5
## Out of Sample: 5
##
## 0-roll forecast [T0=2018 Q4]:
## Series Sigma
## T+1 0.01072 0.008570
## T+2 0.01072 0.008220
## T+3 0.01072 0.007884
## T+4 0.01072 0.007562
## T+5 0.01072 0.007254
## T+6 0.01072 0.006958
## T+7 0.01072 0.006675
## T+8 0.01072 0.006404
## T+9 0.01072 0.006143
## T+10 0.01072 0.005894
